Abstract

Abstract

We investigated the influence of dark matter on light/signal propagation in the solar system. In this paper, we took the effect of solar system-bound dark matter into considerration while the contribution of galactic dark matter was excluded. First, we derived the approximate solution of Einstein equation which consists of the gravitational field due to the central celestial body as the Sun and thin distributed dark matter surrounding to the external region of central body under the spherical symmetry. As the form of dark matter density, we assumed the following power law, ̺(t, r) = ρ(t)(ℓ/r) k where r is the radius from the central body, ℓ is the normalizing factor, k is the exponent characterising r-dependence, and ρ(t) is the function of time t. In accordance with derived approximate solution, we focused on the light propagation and examined the additional corrections due to dark matter on the gravitational time delay and the relative frequency shift. As the application, we considered the secular increasing of the astronomical unit reported by Krasinsky and Brumberg (2004).